Maslov index in Chern-Simons quantum mechanics

1990 ◽  
Vol 42 (8) ◽  
pp. 2763-2778 ◽  
Author(s):  
M. Reuter
Keyword(s):  
Quantum Mechanics ◽  
Maslov Index ◽  
Chern Simons

Chern–Simons gauge theory and symplectic quantum mechanics

2015 ◽  
Vol 93 (9) ◽  
pp. 971-973
Author(s):  
Lisa Jeffrey
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Partition Function ◽  
Partition Functions ◽  
Action Functional ◽  
Symplectic Action ◽  
Chern Simons

We describe the relation between the Chern–Simons gauge theory partition function and the partition function defined using the symplectic action functional as the Lagrangian. We show that the partition functions obtained using these two Lagrangians agree, and we identify the semiclassical formula for the partition function defined using the symplectic action functional. We also compute the semiclassical formulas for the partition functions obtained using the two different Lagrangians: the Chern–Simons functional and the symplectic action functional.

scholarly journals BERRY CONNECTIONS AND INDUCED GAUGE FIELDS IN QUANTUM MECHANICS ON SPHERE

2000 ◽  
Vol 15 (18) ◽  
pp. 1203-1212 ◽  
Author(s):  
HITOSHI IKEMORI ◽  
SHINSAKU KITAKADO ◽  
HIDEHARU OTSU ◽  
TOSHIRO SATO
Keyword(s):  
Quantum Mechanics ◽  
Effective Action ◽  
Degrees Of Freedom ◽  
Gauge Fields ◽  
Chern Simons ◽  
Topological Term

Quantum mechanics on sphere Sn is studied from the viewpoint that the Berry's connection has to appear as a topological term in the effective action. Furthermore we show that this term is the Chern–Simons term of gauge variables that correspond to the extra degrees of freedom of the enlarged space.

Fractional angular momentum in noncommutative generalized Chern-Simons quantum mechanics

2016 ◽  
Vol 131 (7) ◽  
Author(s):  
Xi-Lun Zhang ◽  
Yong-Li Sun ◽  
Qing Wang ◽  
Zheng-Wen Long ◽  
Jian Jing
Keyword(s):  
Quantum Mechanics ◽  
Angular Momentum ◽  
Chern Simons

scholarly journals Chern–Simons quantum mechanics and fractional angular momentum in atom system

2020 ◽  
Vol 35 (22) ◽  
pp. 2050122
Author(s):  
Yao-Yao Ma ◽  
Qiu-Yue Zhang ◽  
Qing Wang ◽  
Jian Jing
Keyword(s):  
Quantum Mechanics ◽  
Dipole Moment ◽  
Angular Momentum ◽  
Kinetic Energy ◽  
Energy Spectra ◽  
Reduced Model ◽  
Full Model ◽  
Specific Setting ◽  
Chern Simons ◽  
Atom System

The model of a planar atom which possesses a nonvanishing electric dipole moment interacting with magnetic fields in a specific setting is studied. Energy spectra of this model and its reduced model, which is the limit of cooling down the atom to the negligible kinetic energy, are solved exactly. We show that energy spectra of the reduced model cannot be obtained directly from the full ones by taking the same limit. In order to get the energy spectra of the reduced model from the full model, we must regularize energy spectra of the full model properly when the limit of the negligible kinetic energy is taken. It is one of the characteristics of the Chern–Simons quantum mechanics. Besides this, the canonical angular momentum of the reduced model will take fractional values although the full model can only take integers. It means that it is possible to realize the Chern–Simons quantum mechanics and fractional angular momentum simultaneously by this model.

scholarly journals Poles in the S-matrix of relativistic Chern-Simons matter theories from quantum mechanics

2015 ◽  
Vol 2015 (4) ◽  
Author(s):  
Yogesh Dandekar ◽  
Mangesh Mandlik ◽  
Shiraz Minwalla
Keyword(s):  
Quantum Mechanics ◽  
S Matrix ◽  
Chern Simons

scholarly journals On a gravity dual to flavored topological quantum mechanics

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrey Feldman
Keyword(s):  
Quantum Mechanics ◽  
Effective Field ◽  
Abjm Theory ◽  
Yang Mills ◽  
Topological Quantum ◽  
Higher Derivatives ◽  
Structure Constants ◽  
Holographic Description ◽  
M Theory ◽  
Chern Simons

Abstract In this paper, we propose a generalization of the AdS2/CFT1 correspondence constructed by Mezei, Pufu and Wang in [1], which is the duality between 2d Yang-Mills theory with higher derivatives in the AdS2 background, and 1d topological quantum mechanics of two adjoint and two fundamental U(N ) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level k = 1. We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [1], which arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in $$ \mathcal{N} $$ N = 4 theory with k fundamental hypermultiplets, having a holographic description as M-theory in the AdS4× S7/ℤk background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory.

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